Question

The radius and height of a cylinder are in the ratio $7:2$. If the volume of the cylinder is $8316c{m}^3$. Find the total surface area of the cylinder.

Answer 1

Let r,h be radius & hight of cylinder

$\Rightarrow volume=\pi r^{2}h,$Total surface area (T.S.A)$=2\pi r(h+r)$

Given. $\frac{r}{h}=\frac{7}{2}\Rightarrow h=\frac{2r}{7}$

Volume =$\pi r^{2}h=8316\Rightarrow \pi r^2\left(\frac{2r}{7}\right)=8316$

$\Rightarrow r^3=\frac{8316\times 7\times 7}{2\times 22}=\frac{7^3\times 1188}{2\times 22}=7^3\times 3^3$

$\Rightarrow r=7\times 3=21cm\Rightarrow h=\frac{2}{7}\times 21=6cm$

T.S.A=$2\pi r=(h+r)=2\times \frac{22}{7}\times 21(6+21)=44\times 3\times 27$

$=3564c{m}^2$